I can’t comment yet, so I’ll tell you here what you can change immediately:
$countryinfo = $wpdb->get_row("SELECT * FROM wp_num_countries WHERE countryID = ".$country_id);
to
$countryinfo = $wpdb->get_row($wpdb->prepare("SELECT * FROM wp_num_countries WHERE countryID = %d", $country_id));
because you directly use $_POST variable, so $wpdb->prepare will format and prepare your query string. But that code looks fine for me (you should only use indents as they are expected, because of easier reading 🙂 )
If I were you, I would make a page and put this code in it. For example, page-countries.php, and page with title Countries, slug ‘countries’. In that form put submit button and that’s it. Also, I would test for if(isset($_POST['country']))
instead of if($_POST['country'])
.